This is probably not the best way to begin 'investigating'. I realize Bauhaus might have been the better way to start. But the whole anti-cross necklace thing has been bugging me for a while. Especially since nu-goths discovered leggings on tumblr.
I've been seeing these symbols (OMG maddness;conspiracy!) and really didn't know where they came from.
Reverse cross:

On face value many people associate it with satanism. In fact, the Church of Satanism doesn't associate with this symbol. I'm not sure if any branches of satanism do, although they may use it to irritate Christians.
This is
actually a Christian symbol of humility. St Peter was crucified upside down because he believed himself unworthy to be crucified as Jesus was. I'm sure there are some Christians out there that disagree, but like every one has their own flavour of goth, every Christian has their own take on Christianity.
(Picture accessed from SymbolDictionary)
Pentagram:

Again, people often associate this with satanism. I think it is associated to an extent, but more often when inverted.
It is a Wiccan/Pagan symbol. It is also a symbol used by both Greeks and Christians. Pythagoras saw it as a way of dividing the human soul (as in fraction, not chopping), the five points representing the five elements. For early Christians it symbolized the wounds sustained by Christ at his crucifixion.
(Picture accessed from
www.thirdcoastrs.com)
Ankh:

The Egyptian hieroglyph for life. It is also known as the 'key of the Nile', 'key of life'
and is associated with rebirth in Egyptian text. Which makes sense, since the Nile
was/is Egypt's life force so to speak. It's also used by the Coptic Orthodox Church who are based in Alexandria.
(Picture accessed from www.hennapaste.de)
Other interesting symbols - (I have no idea if goths wear these. People wear whatever they like, so I suppose someone does)
+ Eye of Horus - An Egyptian hieroglyph and ward against evil

+ Witch's Knot - I think this was sort of, adopted by modern witches, but was originally used as protection against witchcraft (little ironic, eh?) Whether it protects well or not depends on how accurately it's drawn in a single motion.
(Picture accessed from SymbolDictiomary)
I'm sorry if there are any inaccuracies. Feel free to comment if you have a different understanding, opinion or anything to share:)
Sources:
+ Encyclopedia Britannica Online
+ Symbol Dictionary symboldictionary.net
+ GreatScott.com
P.S. If this post was too long, please let me know. Thanks, Sorel:P